Execute stored procedure remotely using linked server

Assuming the procedure lives on the remote server: have you tried using the EXECUTE AT command?

DECLARE @RunStoredProcSQL VARCHAR(1000);
SET @RunStoredProcSQL = 'EXEC [Database].[dbo].[StoredProcName]';
--SELECT @RunStoredProcSQL --Debug
EXEC (@RunStoredProcSQL) AT [LinkedServerName];
Print 'Procedure Executed';

That's what I have used successfully in the past. I usually surround the declare/exec in a try catch just in case, but it's currently working on my systems every hour.